Assignment of channel colors in optical networks

ABSTRACT

A model is provided for optimizing an optical network wherein single links carry multiple signals by using multiple color channels. The routes in the optimized network minimize mid-route color changeovers, reducing the number of nodes requiring optical-electric-optical signal conversion. In the model, the minimized objective function includes terms representing total color miles, terms penalizing changeovers, and terms representing total nodes passed by routes.

FIELD OF THE INVENTION

The present invention relates generally to optical networking, and moreparticularly, to devices, systems and methods to improving theassignment of colors (wavelengths) on individual optical routes. This isaccomplished by the use of an Integer Linear Programming model with themain objective of minimizing color change-over in mid route, thusreducing the need for costly Optical-Electrical-Optical devices whichexecute color change-over.

BACKGROUND OF THE INVENTION

The use of telecommunications networks and associated Network AccessDevices (NADs) has increased dramatically over the last 20 years. Weincreasingly rely on network accessibility for voice, data and videocommunication, now integral to personal, government, business,education, health and safety communications.

In communication networks, a node is an active electronic device that isattached to a network, and is capable of sending, receiving, orforwarding information over a communications channel. A node is aconnection point, either a redistribution point or a communicationendpoint. In network theory, the term node may refer a point in anetwork topology where data links may intersect or branch.

A data link is the means of connecting one location to another for thepurpose of transmitting and receiving digital information. It can alsorefer to a set of electronic assemblies, consisting of a transmitter anda receiver and the interconnecting data telecommunication circuit. Linksare governed by a link protocol enabling digital data to be transferredfrom a data source to a data destination.

Network topology is the study of the arrangement or mapping of thenetwork elements (links, nodes, etc.) of a network, comprised of thephysical (real) and logical (virtual) interconnections between nodes.Local Area Networks (LANs) and Wide Area Networks (WANs) are examples ofnetworks that exhibit both a physical topology and a logical topology.Any given node in a network will have one or more links to one or moreother nodes in the network. Mapping of the links and nodes onto a graphresults in a geometrical shape that determines the physical topology ofthe network. Similarly, the mapping of the flow of data between thenodes in the network determines the logical topology of the network. Thephysical and logical topologies may be identical in any particularnetwork but they also may be different.

High performance and feature-rich communications in a “convergedInternet Protocol” environment may in a single service include privateintranet, voice, video, Internet, and business partner services. Rapidadvances in optical communications technology and devices in terms ofperformance, reliability and cost over the last decade have enabled thedeployment of optically routed Wavelength Division Multiplexing (WDM)networks which can be used to create high capacity nationwide and globalbroadband networks. In these networks, optical signals can flowend-to-end between users, many times without being converted toelectrical signals at the network switches. They can offer largebandwidth, simple cross-connecting of high bit-rate streams, signalformat and bit rate independent clear channels, equipment andoperational savings, as well as maximum flexibility.

Optical networking provides the inter- and intra-transport capabilitiesfor Access, Metropolitan and Global networks. These networks arecomposed of nodes and links, as described above. The links correspond toDWDM (Dense Wave Division Multiplexing) systems with multiple opticalsignals, also called Colors, Wavelengths or Channels. As used herein,color may be used to refer to wavelengths of visible, infrared orultraviolet light. Multiplexing technology continues to evolve whilecurrent methods allow up to 80 discrete colors on a single pair offibers. Nodes may be equipped with Optical Cross Connect devices wherede-multiplexed optical signals are converted from the optical domain tothe electronic domain, switched, converted back to the optical domainand multiplexed optically. This Optical-Electrical-Optical (OEO)function serves two purposes: switching and regeneration of theattenuated optical signals. In contrast Optical Switches operateoptically so that the OEO function needed for regeneration of the signaland possibly for changing wavelength is performed before and/or afterthe optical switching function. Essentially, the optical switch servesas an automated optical patch panel. Also at a node, a ReconfigurableOptical Add/Drop Multiplexer (ROADM) in conjunction with transpondersmay be used to add/drop/switch channels optically.

Links equipped with DWDM systems require optical signal amplificationevery 100-150 kilometers and optical signal regeneration every 1000-1500kilometers. With DWDM systems, all the optical signals can be amplifiedsimultaneously, without de-multiplexing, while regeneration must beperformed on the de-multiplexed optical signals individually.

It would therefore be desirable to develop a system, device and methodto improve the assignment of colors (wavelengths) on individual opticalroutes. By utilizing an Integer Linear Programming model with the mainobjective of minimizing color change-over in mid route, the need forcostly. Optical Cross Connect devices known asOptical-Electrical-Optical devices can be significantly reduced. To theinventors' knowledge, no such system or method currently exists.

SUMMARY OF THE INVENTION

In accordance with a first aspect of the present invention, a method isprovided for assigning colors to WL demands for transmitting multipleoptical signals in an optical network between originating nodes andterminating nodes. The optical network comprises a plurality of nodesinterconnected by a plurality of links, the links each being capable oftransmitting a respective predetermined maximum number of separateoptical signals using separate colors.

In the method, a mathematical model is formulated representing theoptical network and the WL demands. An objective function of the modelis minimized, the objective function representing a total cost of theoptical network as a function of the assignment of colors. The objectivefunction includes a sum of at least the following quantities: a weightedsummation of distances transmitted in each color in the network; aweighted count of each color in each link in each route, and a weightedcount of each color in each route, whereby color changeovers on routesare penalized; and a weighted count of nodes traversed by each route,whereby routes with larger numbers of nodes are penalized. Colors areassigned to the WL demands whereby the objective function is minimized.

Another embodiment of the invention is a computer-usable medium havingcomputer readable instructions stored thereon for execution by aprocessor to perform a method for identifying color channels forassignment to multiple optical signals in an optical network. Thesignals are transmitted over required routes between originating nodesand terminating nodes. The optical network comprises a plurality ofnodes interconnected by a plurality of links, the links each beingcapable of transmitting a respective predetermined maximum number ofseparate optical signals on separate color channels.

The method comprises formulating a mathematical model representing theoptical network and the required routes; and minimizing an objectivefunction of the model, the objective function representing a total costof the optical network as a function of the assignment of colorchannels, the objective function including a sum of at least thefollowing quantities: a weighted summation of distances transmitted ineach color channel in the network; a weighted count of each color ineach link in each route, and a weighted count of each color in eachroute, whereby color changeovers on routes are penalized; and a weightedcount of nodes traversed by each route, whereby routes with largernumbers of nodes are penalized. Color channels are identified forassignment to the multiple optical signals such that the objectivefunction is minimized.

In yet another embodiment of the invention, a method is provided fortransmitting multiple optical signals over separate color channels in anoptical network to satisfy transmission demands between originatingnodes and terminating nodes. The optical network comprises a pluralityof nodes interconnected by a plurality of links, each of the links beingcapable of transmitting a respective predetermined maximum number ofseparate color channels.

The method comprises the steps of partitioning the nodes into geographicclusters whereby all inter-cluster routes have a length less than amaximum regeneration distance; selecting at least one node in eachcluster to contain optical cross connect devices havingoptical-electric-optical converters (OEOs); and routing longerintra-cluster demands via the selected OEO nodes, while ignoring thepredetermined maximum number of separate color channels. For eachcluster, a mathematical model is formulated representing the opticalnetwork, the model further representing all intra-cluster demands andthose portions of inter-cluster demands from their source nodes to anOEO node.

An objective function of the model is minimized, the objective functionrepresenting a total cost of the optical network as a function of theassignment of color channels. Color channels are assigned according tothe minimized objective function; and color channels are assigned to allleftover inter-cluster portions of the demands between their respectiveOEO nodes.

These aspects of the invention and further advantages thereof willbecome apparent to those skilled in the art as the present invention isdescribed with particular reference to the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic of a network including nodes and links inaccordance with an aspect of the present invention;

FIG. 2 shows an exemplary AMPL model, Lambda.mod, to optimize thenetwork of FIG. 1 in accordance with the present invention;

FIG. 3 shows the data, Lambda.dat, and demands for the exemplary AMPLmodel of FIG. 1 in accordance with the present invention;

FIG. 4 shows the run script, Lambda.run, for the exemplary AMPL model ofFIG. 1 in accordance with the present invention;

FIG. 5 shows an output file, Lambda.out, for the exemplary AMPL model ofFIG. 1 in accordance with the present invention;

FIG. 6 shows a partial solution set for color assignment and routes forthe exemplary AMPL model of FIG. 1 in accordance with the presentinvention;

FIG. 7 shows the full solution set for routes only, without colorassignment details, and unused links for the exemplary AMPL model ofFIG. 1 in accordance with the present invention;

FIG. 8 shows an exemplary network to illustrate forced color change-overin mid route in accordance with an aspect of the present invention;

FIG. 9 shows the output of the AMPL model to optimize the network ofFIG. 8 in accordance with the present invention; and

FIG. 10 is a flow diagram of an exemplary method in accordance with anaspect of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

Embodiments of the invention will be described with reference to theaccompanying drawing figures wherein like numbers represent likeelements throughout. Before embodiments of the invention are explainedin detail, it is to be understood that the invention is not limited inits application to the details of the examples set forth in thefollowing description or illustrated in the figures. The invention iscapable of other embodiments and of being practiced or carried out in avariety of applications and in various ways. Also, it is to beunderstood that the phraseology and terminology used herein is for thepurpose of description and should not be regarded as limiting. The useof “including,” “comprising,” or “having” and variations thereof hereinare meant to encompass the items listed thereafter and equivalentsthereof as well as additional items.

The present invention describes an optical communications networkoptimization model to assign colors to routes carrying optical signaldemands (traffic) in order to minimize the need to change colors inmid-route. There are several variants of the model, a ‘static’ one inwhich all demands are given input, a ‘dynamic’ one in which additionaldemands need assignments without (or minimally) rearranging currentassignments, and a ‘restoration’ one in which a link or some colors on alink fail and the disrupted demands need to be reassigned routes andcolors, again without (or minimally) rearranging existing functionalassignments. The model provides a basic construct which may be modifiedby removing irrelevant variables or constraint sets, or extended bybuilding upon the basic model, as needed.

The present invention pertains mainly to modeling optical communicationsnetwork traffic in an optical mesh network, and has much in common withthe problem of finding diverse routes in a network. In this regard,finding link-disjoint routes for demands are considered. These routesare assigned colors but they may cross at nodes where routes intersect,a function provided by an Optical Switch.

A route ‘r’ is defined by binary variables x[l, r] where the ‘l’-sidentify the links that the route ‘r’ traverses. To solve for the valuesof x[l, r], a special case of the standard single-commodity capacitatednetwork-flow approach in an arc-node formulation is used. A directedlink ‘l’ is represented on a graph as an arc from node ‘i’ to node ‘j’.Associated with a link is a cost per unit flow c[l], (say distance orlatency) and a flow variable x[r, l]. Associated with every route ‘r’,is a source node ‘a’ with an in-flow of one unit and destination node‘z’ with out-flow of one unit. Nodes that are neither a source nor adestination conserve flows. A Linear Programming model that minimizesΣx[l,r]*c[l] subject to conservation of flow equations in an arc-nodeformulation will result in x[l, r]={0, 1} defining the shortest path for‘r’ from ‘a’ to ‘z’. Additionally, constraints will be added to theformulation to accommodate the need to assign colors to each route.Furthermore, variables and constraint sets are added to solve severalclosely related problems. Finally, weights are then used in theobjective function to direct the solution.

FIG. 1 is a schematic 100 of a network comprising nodes and links inaccordance with an aspect of the present invention. The network 100consists of 10 nodes, denoted by numbers within boxes and 24 links,denoted by numbers on bi-directional arrows. The links connect thenodes. For example, bi-directional link number 13 connects node 4 withnode 6, and bi-directional link number 5 connects node 2 with node 4.

For modeling purposes each link of FIG. 1 is represented as twouni-directional links, thus the 24 bi-directional links end uprepresented as 48 unidirectional ones. Bi-directional link 13 isassociated with the unidirectional link 13 (and ordered node-pair 4-6)and with the unidirectional link 37 (=13+24) and with the orderednode-pair 6-4. Similarly, unidirectional link 2 is associated with nodepair 1-10 and unidirectional link 26 (=2+24) with node pair 10-1. A linkcorresponds to a DWDM system connecting the pair of nodes.

DWDM systems typically consist of two directional streams of bits on twofibers; however, some systems may use only one fiber for bothdirections. As related to the model, the two directions associated witheach link are required to help determine routes and they do notcorrespond to the directions of the bits.

The model of the present invention as described with reference to FIG. 1assumes that all DWDM systems are identical and have identical channelcapacity (i.e. have the same number of colors). The model can beextended without departing from the present invention to accommodateDWDMs with a varying number of colors and can accommodate parallelsystems between pairs of nodes. Demands are given in units of wavelengthbetween pairs of nodes. The model will determine a route for each demandand assign colors one per unit of demand, subject to availability ofcolors while minimizing color changeover mid route.

In what follows, the model will be defined using the syntax of AMPL (AMathematical Programming Language), as is known by those skilled in theart. Other programming languages may be used. First the input data willbe defined, followed by the variables, then the set of constraints andfinally the objective function.

Data

The number of nodes in the network is defined, together with the set ofnodes and their numerical identities.

======= param NUMNODES ; # number of nodes set NN := 1..NUMNODES ; # setof nodes param NODES {n in NN}; # node IDs =======

The data associated with the links are defined in the uni-directionalmanner described earlier. The first set from 1 to NUMLINKS have aforward direction and the ones from NUMLINKS+1 to 2*NUMLINKS theassociated backwards direction. Whenever referring to bidirectionallinks, the first set only will be used. Thus, link 1 and link 1+NUMLINKSrepresent the two directions of link 1. Note that the links and theirassociated data may have the same end-nodes provided they have distinctlink numbers; that is, multiple DWDM systems between same pairs ofend-nodes must have distinct link numbers in the set L.

======= param NUMLINKS ; param NUMLINKS2 := 2*NUMLINKS; set L :=1..NUMLINKS;   # set of links a to z set L2 := 1..NUMLINKS2; # set oflinks a to z and z to a =======

The next set of data is associated with each directed link. That dataincludes the identities of its originating node, terminating node andits distance.

The number of allowed colors per link is then defined in L (DWDM) andtheir identity in the set CC.

======= param LO {l in L2}; # links' originating nodes param LD {l inL2}; # links' destination nodes param DIST {l in L2};   # distance ofeach link param NUMCOLORS; # number of colors (wavelengths) assumed thesame for each link set CC := 1..NUMCOLORS; # set of colors ========

Data for the requested routes is then specified, including the number ofroutes, their end-nodes and associated wavelength requirement (in unitsof wavelength). The model attempts to assign a color to each unit andall colors will follow the same route for a specific demand requirement.Note that one could request several routes with the same end node-pairs.In this case the model will attempt to generate several routes possiblydistinct, while minimizing the total distance.

For each node, the minimum number of via routes the node shouldaccommodate and the maximum number of total wavelengths (WLs) the nodecan accommodate as via capacity are specified. These parameters, as usedin the following constraints, provide a way to designate some nodes asOEO nodes.

The MAXHOP parameters can be used to constrain the number of hops on aroute and the Wx parameters are used as weights for different terms inthe objective function.

============== param NUMR ; # number of demand requirements set R :=1..NUMR; param RO {r in R}; # set of a requirements’ originating endpoint param RD {r in R}; # set of a requirements’ destination end pointsparam WL {r in R}; # number of wavelength demand requirement (in lambdaunits) param NUMVIA {n in NN}; # forcing routes via a switch for OEOfunctionality param NUMVIACAP {n in NN}; # constraining total WLs via aswitch param MAXHOP ; # max number of hops allowed on route param W1; #weights for terms in the objective function param W2; param W3; paramW4; param W5; ==========

Variables

The x variables, when set to 1 by the program for route r and link 1,define the links that make the route. The auxiliary variables uu and vvwill be used to force consistency of color along a route. The variablezz indicates the use of a color in the network. The variable via whenset to 1 indicates that route r traverses node n. This will be explainedlater when describing the constraint sets and how it is being used.

========== var x{l in L2, r in R}, binary; # =1 if route r uses link l,0 otherwise var uu{ r in R, l in L2, c in CC}, binary; # colorassignment variable var vv{ r in R, c in CC}, binary;  # upper boundvariable to force color consistency Var zz{c in CC) >=0, integer; #color use indicator var via{n in NN, r in R} >=0;  # computed variableif =1 then # route r traverses node n ==========

Constraints

The first three sets of constraints are structured to define routes. Foreach requested route r, the traditional set node flow-conservationequations with a balance of {+1, −1, 0} depending on whether the node isan originating one, terminating one or either flow-thru node ornon-participating one for the route. This formulation alleviates theneed to pre calculate large sets of potential routes.

The 4^(th) set of constraints is based on the third set. The variablevia[n,r] is computed and it takes a value of 1 if route r passes vianode n, or is 0 otherwise. This variable can be used to force a route touse or avoid a set of particular nodes to be defined in the input datafile.

The 5^(th) and 6^(th) sets of constraints force a minimum of NUMVIA[n]routes to pass thru node n not to exceed a total of NUMVIACAP[n} unitsof WLs.

An optional 7^(th) set of constraints limits the total number of hops oneach route, for example to no more than MAXHOP. Slight modifications ofthe 7^(th) set of constraints can accommodate limits on route miles ormaximum permitted latency for each demand (route). This constraint maybe used to reflect technological limitations in the network.

================ subject to node_conserve1 {n in NN, r in R : n=RD[r]}:  sum {l in L2, m in NN : n=LO[l] && m=LD[l]} x[l,r]   − sum {l in L2, min NN : n=LD[l] && m=LO[l]} x[l,r] = −1; subject to node_conserve2 {n inNN, r in R : n=RO[r]}:   sum {l in L2, m in NN : n=LO[l] && m=LD[l]}x[l,r]   − sum {l in L2, m in NN : n=LD[l] && m=LO[l]} x[l,r] = 1;subject to node_conserve3 {n in NN, r in R : n <> RO[r] && n <> RD[r]}:  sum {l in L2, m in NN : n=LO[l] && m=LD[l]} x[l,r]   − sum {l in L2, min NN : n=LD[l] && m=LO[l]} x[l,r] = 0 ; subject to flowthru {n in NN, rin R : n <> RO[r] && n <> RD[r]}:   sum {l in L2, m in NN : n=LO[l] &&m=LD[l]} x[l,r]   + sum {l in L2, m in NN : n=LD[l] && m=LO[l]} x[l,r] =  2*via[n,r] ; subject to total_via{n in NN}:   sum {r in R} via[n,r] >=NUMVIA[n]; subject to node_via_cap{n in NN}:   sum {r in R} via[n,r] *WL[r] <= NUMVIACAP[n]; subject to maxhop {r in R}:   sum {l in L2}x[l,r] <= MAXHOP; =================

The following set of equations assures that capacity of each link is notexceeded. Notice that each demand is associated with a route and doesnot get split across routes. If splitting is allowed then eachwavelength request is for one unit (WL[r]=1) and the model stillapplies.

======================== # defined for nondirectional links subject tocapacity_cons {l in L}: sum {r in R} (x[l,r] +x[l+NUMLINKS,r])*WL[r] <=NUMCOLORS ========================

The set of inequalities that force contiguities of colors along theroutes follows. The variable uu[r,l,c] is binary and assigns a specificcolor ‘c’ on link ‘l’ when used by route ‘r’. The first set ofconstraints, ‘uu_color’, assures proper distribution of colors for eachchannel in the demand set of route ‘r’. The second set of constraints,‘vv_color’, counts the number of colors that has been used up bydifferent links on the same route. These variables uu[r,l,c] and vv[r,c]will be used in the objective function to force, if possible, anassignment of one color per route by associating a weight with vv[r,c].Notice that when vv[r,c]=1, route ‘r’ is assigned color ‘c’. Whenvv[r,c]=2, two colors are associated with route ‘r’, but the number ofcolor changeovers at nodes on the route could be ≧1. For example, aroute with 5 links that have been assigned 2 colors (1 and 2) could haveat most 4 changeovers (1, 2, 1, 2, 1).

======================== # forcing contiguous color # distinct colorsare assigned by uu[r,l,c] # maintaining continuity of colors usingvv[r,c] # only one color can be assigned per link (forward and backwardsdirection # counting the number of colors used in the network subject touu_color {l in L2, r in R}:   x[l,r]*WL[r] = sum {c in CC} uu[r,l,c];subject to vv_color { r in R, l in L2, c in CC}:   uu[r,l,c] <= vv[r,c];subject to wl_color { l in L , c in CC}:   sum {r in R}(uu[r,l,c]+uu[r,l+NUMLINKS,c]) <=1; subject to zz_color ( r in R, l inL, c in CC }:   uu[r,l,c] <= zz[c]; ========================

The last set of constraints indicates the use of a color ‘c’ and thevariable zz[c] and its weight W5 may be used in the objective functionto force a solution with a minimum number of colors in the network.

Objective Function

In the following objective function, the first summation represents thetotal wavelength miles. The second and third terms use penalties tominimize color changeovers on routes. The fourth term minimizes thenumber of nodes passed by the routes. The fifth term may be used tominimize color use in the network.

minimize color_cost:

${{{sum}\begin{Bmatrix}{{r\mspace{14mu} {in}\mspace{14mu} R},} \\{1\mspace{14mu} {in}\mspace{14mu} L}\end{Bmatrix}W\; 1*{{WL}\lbrack r\rbrack}*{{DIST}\lbrack l\rbrack}*\begin{pmatrix}{{x\lbrack {1,r} \rbrack} +} \\{x\lbrack {{1 + {NUMLINKS}},r} \rbrack}\end{pmatrix}} + {{sum}\begin{Bmatrix}{{r\mspace{14mu} {in}\mspace{14mu} R},} \\{{l\mspace{14mu} {in}\mspace{14mu} L\; 2},} \\{c\mspace{14mu} {in}\mspace{14mu} {CC}}\end{Bmatrix}W\; 2*{{uu}\lbrack {r,l,c} \rbrack}} + {{sum}\begin{Bmatrix}{{r\mspace{14mu} {in}\mspace{14mu} R},} \\{c\mspace{14mu} {in}\mspace{14mu} {CC}}\end{Bmatrix}W\; 3*{{vv}\lbrack {r,c} \rbrack}} + {{sum}\begin{Bmatrix}{{n\mspace{14mu} {in}\mspace{14mu} {NN}},} \\{r\mspace{14mu} {in}\mspace{14mu} R}\end{Bmatrix}W\; 4*{{via}\lbrack {n,r} \rbrack}} + {{{sum}( {c\mspace{14mu} {in}\mspace{14mu} {CC}} \}}{W5}*{{zz}\lbrack c\rbrack}}};$

Scalability

The model can grow very large in terms of the number of variables andconstraints.

Number of variables:

x[l,r] 2*L*R uu[r,l,c] R*2*L*C vv[l,c] 2*L*C zz[c] C via[n,r] N*R

Number of constraints:

node_conserve N*R flowthru N*R total_via N total_via_cap N max_hop Ruu_color 2*L*R vv_color R*2*L*C wl_color L*C zz_color R*L*C color_cost 1

The model produced results quickly for a small sample network (such asthe example of FIG. 1, where N=10, L=24, R=8 and C=4), with larger andmore complex networks having longer run times.

Some additional measures may be required if the underlying network getsto be orders of magnitude larger, such as:

-   -   a) use of a faster multi-processing machine;    -   b) processing routing requests only off-line for planning        purposes;    -   c) terminating a program run before optimality is proven by the        branch and bound method; and    -   d) reverting to pure LP and integerize fractional variables with        a post-processing heuristics.

The following describes two scenarios to improving the assignment ofcolors (wavelengths) on individual optical routes in accordance withaspects of the present invention.

Example 1 Optimization of the FIG. 1 Network

One example of optimization of color use in the network of FIG. 1 ispresented in FIGS. 2-5. A listing of the AMPL model, Lambda.mod 200, isshown in FIG. 2. A listing of the data for the network of FIG. 1,Lambda.dat 300, including the demands for 8 routes, is shown in FIG. 3.A listing of a run script, Lambda.run 400, is shown in FIG. 4. An outputfile, Lambda.out 500, is shown in FIG. 5. This optimization was solvedwith virtually no delay in 1938 Mixed Integer Program (MIP) simplexiterations and 0 branch-and-bound nodes.

The following is the output of a previous run that had no zz variablesand no fifth term in the objective function. That run was solved withvirtually no delay in 2075 MIP simplex iterations and 10branch-and-bound nodes. FIG. 6 shows a partial color assignment solutionset 600 for the exemplary AMPL model run.

For this optimization solution shown in FIG. 6, the demands are asfollows:

param: RO RD WL := 1 1 10 4 2 10 1 3 3 6 3 4 4 2 8 4 5 9 4 1 6 10 1 3 76 3 2 8 2 8 1 ;

From the above table, demand number 1 from node 1 to node 10 is for 4units and demand number 2 from node 10 to node 1 is for 3 units. Demandnumber 6 from node 10 to node 1 is for 3 units. These demands willfollow 3 routes, link-capacities permitting.

For this optimization solution, the output matrix is as follows:

vv[r,c] [*,*] : 1 2 3 4 := 1 1 1 1 1 2 . 1 1 1 3 1 1 1 1 4 1 1 1 1 5 1 .. . 6 1 1 . 1 7 1 1 . . 8 . . 1 . ;

The output matrix indicates that demand number 1 for 4 units wasassigned colors 1, 2, 3 and 4 on its route (no splitting assumption),and demand number 2 for 3 units was assigned colors 2, 3 and 4 on aseparate route. Since no entry in this matrix is greater than 1, it isconcluded that a solution was found without a need to switch colors inmid-route.

The following matrices indicate the assignment of colors on the linksfor each unit of WL by route.

uu[r,l,c] [*,*,1] (tr) : 1 3 4 5 6 7 :=  2 1 . . . . .  6 . . 1 . . . 15. . 1 . . . 17 . 1 . . . . 18 . . . . . 1 23 . . . . . 1 27 . . . . 1 .29 . . . . 1 . 34 . 1 . . . . 35 . . . 1 . . 37 . . . . 1 . 40 . 1 . . .. 44 . . . . . 1 48 . . . . 1 . [*,*,2] (tr) : 1 2 3 4 6 7 :=  2 1 . . .. .  6 . . . 1 . . 15 . . . 1 . . 17 . . 1 . . . 18 . . . . . 1 21 . 1 .. . . 23 . . . . . 1 25 . 1 . . . . 27 . . . . 1 . 29 . . . . 1 . 34 . .1 . . . 35 . 1 . . . . 37 . . . . 1 . 40 . . 1 . . . 44 . . . . . 1 48 .. . . 1 . [*,*,3] (tr) : 1 2 3 4 8 :=  2 1 . . . .  5 . . . . 1  6 . . .1 . 13 . . . . 1 15 . . . 1 . 17 . . 1 . . 18 . . . . 1 21 . 1 . . . 25. 1 . . . 34 . . 1 . . 35 . 1 . . . 40 . . 1 . . [*,*,4] (tr) : 1 2 3 46 := 2 1 . . . . 6 . . . 1 . 15 . . . 1 . 17 . . 1 . . 21 . 1 . . . 25 .1 . . . 27 . . . . 1 29 . . . . 1 34 . . 1 . . 35 . 1 . . . 37 . . . . 140 . . 1 . . 48 . . . . 1 ;

Routes satisfying four of the eight demands are shown in FIG. 6. Link 2was used for the first route and consumed all 4 colors for demand number1 from node 1 to node 10. Colors 2, 3 and 4 were used for demand number2 (of three units) on the route composed of links 21, 35 and 25 (that is21, 11 and 1) from node 10 to node 1. Demand number 7 from node 6 tonode 3 for two units was assigned colors 1 and 2 on the route composedof links 18, 44 and 23 (that is 18, 20 and 23). Demand number 6 againfrom node 10 to node 1 consumes colors 1, 2 and 4 on links 48, 37, 29,and 27 (24, 13, 5 and 3).

FIG. 7 shows the full solution set 700 for all eight demands for theexemplary AMPL model. The lines correspond to the routes only and not tothe assignment of colors to WL's. The diagram of FIG. 7 explains whatseems to be inefficient routing of demands 2, 6 and 7. Each route(demand) represents several WL's. There is clearly a mismatch betweenthe demands and the link capacities. Longer routes may result fromeither lack of capacities or from the requirement for color contiguityof WL.

The matrix via[n,r]:

via[n,r] [*,*] : 1 2 3 4 5 6 7 8 :=  1 0 0 0 0 0 0 0 0  2 0 0 0 0 0 1 00  3 0 0 0 0 0 0 0 0  4 0 1 0 0 0 1 0 1  5 0 0 1 1 0 0 0 0  6 0 0 0 0 01 0 1  7 0 0 1 0 0 0 0 0  8 0 0 0 0 0 0 1 0  9 0 1 0 0 0 0 1 0 10 0 0 00 0 0 0 0 ;

From the above matrix, demand number 1 is routed directly without vianodes. Demand number 2 passes via nodes 4 and 9; demand number 6 vianodes 2, 4 and 6; and demand number 7 passes via nodes 8 and 9. Thesefour demands and corresponding individually assigned colors wereillustrated in detail in FIG. 6.

Example 2 Forced Color Change-Over in Mid Route

To illustrate forced color changes on a route, a small example ispresented in FIGS. 8 and 9. FIG. 8 shows an exemplary network 800 toillustrate forced color change-over in mid route in accordance with anaspect of the present invention. The exemplary network consists of 4nodes, 6 bi-directional links, 3 demands for 1 unit of wavelength each,with every link able to accommodate 2 colors, as follows:

======= param NUMNODES :=4; param NUMLINKS :=3; param :LO LD DIST:= 1 12 100 2 1 3 100 3 1 4 100 4 2 3 140 {close oversize brace} Forward 5 2 4140 6 3 4 140 7 2 1 100 8 3 1 100 9 4 1 100 10 3 2 140 {close oversizebrace} Backward 11 4 2 140 12 4 3 140 param NUMCOLORS :=2; param NUMR:=3 param : RO RD WL := 1 2 3 1 2 2 4 1 3 3 4 1; param: NUMVIANUMVIACAP:= 1 3 3 2 0 3 3 0 3 4 0 3 =======

The output of the model for example 2 is shown in FIG. 9, and shownbelow are matrices uu[r,l,c] and via[n,r].

uu[r,l,c] := 1 2 2 1 1 7 2 1 2 3 2 1 2 7 1 1 3 3 1 1 3 8 1 1 via[n,r] :=1 1 1 1 2 1 1 3 1 2 1 0 2 2 0 2 3 0 3 1 0 3 2 0 3 3 0 4 1 0 4 2 0 4 3 0

The matrix uu[r,l,c] shows that demand route number 1 (element 910 ofFIG. 9) was assigned color 2 on both link 2 920 and link 1 930. Demandroute number 3 (element 940) was assigned color 1 on both link 2 950 andlink 3 960. Lastly, demand route 2 970 was assigned color 2 on link 3980 and color 1 on link 1 990. A color changeover was executed in node 1for demand route 2 970. The output matrix via[n,r] shows that all threedemands were forced via node 1 and nodes 2, 3 and 4 have no via routes.

FIG. 10 is a flow diagram of an exemplary method 1000 in accordance withone aspect of the present invention. In step 1010 a mathematical modelis formulated representing the optical network and the WL demands;

An objective function of the model is then minimized (step 1020). Theobjective function represents a total cost of the optical network as afunction of the assignment of color channels. In a preferred embodiment,the objective function includes a sum of at least the followingquantities: a weighted summation of distances transmitted in each colorchannel in the network; a weighted count of each color in each link ineach route, and a weighted count of each color in each route, wherebycolor changeovers on routes are penalized; and a weighted count of nodestraversed by each route, whereby routes with larger numbers of nodes arepenalized.

Colors are assigned (step 1030) to the WL demands whereby the objectivefunction is minimized.

Variants and Extensions

As mentioned earlier, the model is basic but may be extended in severaldirections. Assumptions are made, for example, that the channel unitsare fixed (e.g. OC48) but the model can be extended to DWDMs havinglink-dependent numbers of channels.

If a change in color is required, the model assumes it can take place inany node. With added complexity one can define two types of nodes: onetype can provide changing of colors functionality and the other doesnot. The structure of the set of hop constraints can be used to setbounds on route mileage and a bound on latency.

Extensions already discussed include requirements that force routes totraverse designated OEO nodes or minimize total color usage in thenetwork.

One benefit of the present invention is that the model minimizes therequirement for costly OEO devices when amplification suffices (withinthe limitation of distance). Furthermore, it provides for a structure sothat additional extensions and enhancements could be added as needed ortechnology changes make possible or feasible. For example, one could 1)partition the nodes of a network into geographical clusters that assurethat all intra-cluster routes satisfy the regeneration distanceconstraints, 2) select say 2 nodes (for reliability) from each suchcluster as OEO nodes, 3) route all intra-cluster ‘long’ demands via theOEO nodes ignoring temporarily the color constraints 4) use the currentmodel, a cluster at a time, to route the intra-cluster demands and thepartial demands of the inter-cluster demands from their source nodes tothe cluster's OEO node identified in (3), and 5) assign colors to allthe leftover inter-cluster portions of the demands between theirrespective OEOs.

In the model of the present invention, all demands are given as inputdata while the output presents an optimal assignment of colors. This isa ‘static’ greenfield problem, as known by those skilled in the art. A“dynamic” version of the problem assumes that an assignment is alreadyin place and there are new requests for some additional demands. In a‘restoration’ version of the problem a link or some WL's on a link fail,thus the routes fail. In the content of the model of the presentinvention, for the ‘dynamic’ and ‘restoration’ cases, one can fix thevariables x[l,r] and uu[r,l,c] at value l for the routes that that stayup and re-solve the model for the disrupted, new demands or the oncethat can be rearranged.

The foregoing detailed description is to be understood as being in everyrespect illustrative and exemplary, but not restrictive, and the scopeof the invention disclosed herein is not to be determined from thedescription of the invention, but rather from the claims as interpretedaccording to the full breadth permitted by the patent laws. It is to beunderstood that the embodiments shown and described herein are onlyillustrative of the principles of the present invention and that variousmodifications may be implemented by those skilled in the art withoutdeparting from the scope and spirit of the invention.

1. A method for assigning colors to WL demands for transmitting multipleoptical signals in an optical network between originating nodes andterminating nodes, the optical network comprising a plurality of nodesinterconnected by a plurality of links, the links each being capable oftransmitting a respective predetermined maximum number of separateoptical signals using separate colors, the method comprising:formulating a mathematical model representing the optical network andthe WL demands; minimizing an objective function of the model, theobjective function representing a total cost of the optical network as afunction of the assignment of colors, the objective function including asum of at least the following quantities: a weighted summation ofdistances transmitted in each color in the network; a weighted count ofeach color in each link in each route, and a weighted count of eachcolor in each route, whereby color changeovers on routes are penalized;and a weighted count of nodes traversed by each route, whereby routeswith larger numbers of nodes are penalized; and assigning colors to theWL demands whereby the objective function is minimized.
 2. The method ofclaim 1, wherein the objective function sum further includes: a weightedcount of different colors used in the network, whereby the number ofcolors used is minimized.
 3. The method of claim 1, wherein themathematical model comprises a forward link and a reverse link betweeneach pair of nodes.
 4. The method of claim 1, wherein the mathematicalmodel comprises a constraint set for defining routes whereby a minimumnumber of routes pass through any given node.
 5. The method of claim 4,wherein the constraint set for defining routes defines a maximum numberof routes passing through any given node.
 6. The method of claim 4,wherein the constraint set for defining routes defines a maximum numberof hops in any given route.
 7. The method of claim 1, wherein themathematical model comprises a constraint set for assuring adequate linkcapacity whereby a minimum number of routes pass through any given node.8. The method of claim 1, wherein the predetermined maximum number ofseparate optical signals using separate colors is common for all links.9. The method of claim 1, wherein the predetermined maximum number ofseparate optical signals using separate colors is different between atleast two links.
 10. The method of claim 1, wherein the step offormulating a mathematical model representing the optical network andthe WL demands further comprises designating certain of the nodes asoptical cross connect devices having optical-electric-opticalconverters.
 11. The method of claim 10, wherein the nodes designated asoptical cross connect devices are designated by specifying, for thosenodes, a minimum number of accommodated via routes and a maximum numberof total colors accommodated as via capacity.
 12. A computer-usablemedium having computer readable instructions stored thereon forexecution by a processor to perform a method for identifying colorchannels for assignment to multiple optical signals in an opticalnetwork, the signals being transmitted over required routes betweenoriginating nodes and terminating nodes, the optical network comprisinga plurality of nodes interconnected by a plurality of links, the linkseach being capable of transmitting a respective predetermined maximumnumber of separate optical signals on separate color channels, themethod comprising: formulating a mathematical model representing theoptical network and the required routes; minimizing an objectivefunction of the model, the objective function representing a total costof the optical network as a function of the assignment of colorchannels, the objective function including a sum of at least thefollowing quantities: a weighted summation of distances transmitted ineach color channel in the network; a weighted count of each color ineach link in each route, and a weighted count of each color in eachroute, whereby color changeovers on routes are penalized; and a weightedcount of nodes traversed by each route, whereby routes with largernumbers of nodes are penalized; and identifying color channels forassignment to the multiple optical signals such that the objectivefunction is minimized.
 13. The computer useable medium of claim 12,wherein the objective function sum further includes: a weighted count ofdifferent color channels used in the network, whereby the number ofcolor channels used is minimized.
 14. The computer useable medium ofclaim 12, wherein the mathematical model comprises a forward link and areverse link between each pair of nodes.
 15. The computer useable mediumof claim 12, wherein the mathematical model comprises a constraint setfor defining routes whereby a minimum number of routes pass through anygiven node.
 16. The computer useable medium of claim 15, wherein theconstraint set for defining routes defines a maximum number of routespassing through any given node.
 17. The computer useable medium of claim12, wherein the mathematical model comprises a constraint set forassuring adequate link capacity whereby a minimum number of routes passthrough any given node.
 18. The computer useable medium of claim 12,wherein the predetermined maximum number of separate optical signals onseparate color channels is common for all links.
 19. The computeruseable medium of claim 12, wherein the predetermined maximum number ofseparate optical signals on separate color channels is different betweenat least two links.
 20. A method for transmitting multiple opticalsignals over separate color channels in an optical network to satisfytransmission demands between originating nodes and terminating nodes,the optical network comprising a plurality of nodes interconnected by aplurality of links, each of the links being capable of transmitting arespective predetermined maximum number of separate color channels, themethod comprising: partitioning the nodes into geographic clusterswhereby all inter-cluster routes have a length less than a maximumregeneration distance; selecting at least one node in each cluster tocontain optical cross connect devices having optical-electric-opticalconverters (OEOs); routing longer intra-cluster demands via the selectedOEO nodes, while ignoring the predetermined maximum number of separatecolor channels; for each cluster, formulating a mathematical modelrepresenting the optical network, the model further representing allintra-cluster demands and those portions of inter-cluster demands fromtheir source nodes to an OEO node; minimizing an objective function ofthe model, the objective function representing a total cost of theoptical network as a function of the assignment of color channels; andassigning color channels according to the minimized objective function;and assigning color channels to all leftover inter-cluster portions ofthe demands between their respective OEO nodes.